Federal Reserve Chairwoman Janet Yellen said the central bank doesn’t have the authority to regulate bitcoin.

“The Federal Reserve simply does not have authority to supervise or regulate bitcoin in any way,” Ms. Yellen said Thursday in testimony before the Senate Banking Committee. “This is a payment innovation that is taking place entirely outside the banking industry and to the best of my knowledge there is no intersection at all” between bitcoin and banks that the Fed can oversee.

Bitcoin prices recently fell 1% to $571.29, according to the CoinDesk price index that tracks two virtual-currency exchanges. That’s down from about $700 at the beginning of the year and more than $1,100 in early December.

Ms. Yellen said “it certainly would be appropriate, I think, for Congress to ask questions to what the right legal structure would be” for overseeing the new currency. But she said the issue could pose challenges for lawmakers.

“It’s not so easy to regulate bitcoin because there is no central issuer or network operator to regulate,” she said in response to questions by Sen. Joe Manchin (D., W.Va.), who previously called on U.S. regulators to impose stricter limits on bitcoin.

In a letter released Wednesday to regulators and Treasury Secretary Jacob Lew, Mr. Manchin said: “I am most concerned that as Bitcoin is inevitably banned in other countries, Americans will be left holding the bag on a valueless currency.”

Wall Street analysts have also raised concerns about bitcoin. In a note to clients on Wednesday, Citigroup currency strategist Steven Englander said bitcoin has become “even more speculative” following the Mt. Gox shutdown. “One question is whether the decentralized structure, which is the attraction to many, makes it too cumbersome to enact essential fixes.”